Max Tegmark explicitly rejects physical infinity. http://blogs.discovermagazine.com/crux/2015/02/20/infinity-ruining-physics/ I must add that I'm always a little confused when someone says, "Check out X" where X is a prolific scientist with dozens if not hundreds of books and papers and articles on a variety of subjects to their credit. Which of Tegmark's many accomplishments are you referring to? I get that feeling too. He's interesting and provocative, but I don't think he expects his speculative ideas to be taken as actual science. He's probably amused that people take his mathematical universe idea seriously. I'm not a physicist so I'll let this article explain why physicists like Hilbert space. It uses a lot of buzzwords but I can't simplify it. Perhaps one of the physics-minded folks here can do a better job. https://www.researchgate.net/post/Why_is_the_Hilberts_space_useful_in_quantum_mechanics From a mathematical point of view, Hilbert space is first, an infinite-dimensional vector space. Just like the reals are a one-dimensional vector space, and the plane is a 2-dimensional vector space, Hilbert space has infinitely many dimensions. Two, it admits an inner product, which generalizes the dot product from multivariable calculus. And three, it's complete, meaning there are no holes in it. The real numbers are complete, meaning that every sequence that "should" converge does converge. The rational numbers are no complete, because there are holes where the irrationals should be. It's the completeness that's the most un-physical aspect of Hilbert space and, for that matter, the standard and familiar real numbers. Most real numbers encode an infinite amount of information and can not be computed or described by any algorithm or computer program. The real numbers are extremely UNreal. It's virtually impossible to make a claim that the real numbers represent anything in the physical world. Yet all of physics from Newton onward are based on the real numbers, which require the concept of infinite sets to get off the ground. It's an actual philosophical problem, not always recognized by the physicists themselves.